WASHINGTON — House Democrats on Tuesday unveiled a $3 trillion pandemic relief measure, an ambitious package with aid for struggling states and another round of direct payments to Americans that Republicans instantly dismissed as an exorbitantly priced and overreaching response to the coronavirus crisis.

The proposal, which spanned 1,815 pages, would add a fifth installment to an already sweeping assistance effort from the federal government, although its cost totaled more than the four previous measures combined. And unlike those packages, which were the product of intense bipartisan negotiations among lawmakers and administration officials who agreed generally on the need for rapid and robust action, the House bill represents an opening gambit in what is likely to be a bracing fight over what is needed to counter the public health and economic tolls of the pandemic.

It included nearly $1 trillion for state, local and tribal governments and territories, an extension of unemployment benefits and another round of $1,200 direct payments to American families. The measure would also provide a $25 billion bailout for the Postal Service — which the beleaguered agency has called a critical lifeline, but President Trump has opposed — and $3.6 billion to bolster election security.

“There are those who said, ‘Let’s just pause,’ ” said Speaker Nancy Pelosi of California, invoking a word used by Senator Mitch McConnell, Republican of Kentucky and the majority leader, who has said lawmakers should “push the pause button” on further coronavirus aid. “The families who are suffering know that hunger doesn’t take a pause. The rent doesn’t take a pause. The bills don’t take a pause. The hardship of losing a job or tragically losing a loved one doesn’t take a pause.”

Senate Republicans immediately rejected the measure. But the House will return to Washington on Friday to approve it, Democratic leaders said, along with historic changes to the chamber’s rules that will allow lawmakers for the first time to vote without being physically present in the Capitol.

The measure from House Democrats underscored the gulf between the two parties over how to respond to the coronavirus crisis. Economists and policy experts warn that the government’s relief efforts to date — as unparalleled and far-reaching as they have been — have barely sustained individuals and companies affected by the pandemic, and that abandoning them could result in a deep and protracted recession.

But Republicans and the White House have begun to argue that a new round of relief should wait, and Mr. McConnell has said any such aid must be paired with a measure to give companies sweeping protections from a wide range of potential lawsuits as they try to reopen during the pandemic. Mr. Trump and White House officials have also indicated they want any further economic aid legislation to contain tax cuts, although they have yet to agree on which ones to pursue.

Democrats are headed in the other direction, as Ms. Pelosi suggested in a letter this week in which she encouraged her colleagues to “think big” about additional federal aid. Democratic leaders initially drafted a $4 trillion relief package, she told Democrats on a private phone call on Tuesday morning, but ultimately narrowed the scope, according to a Democrat on the call. The exchange was first reported by Politico.

Even before Democrats presented their proposal on Tuesday, top Senate Republicans were voicing vehement opposition, urging restraint in doling out another substantial round of taxpayer dollars as the federal government and banks scramble to distribute the funds from the $2.2 trillion stimulus law enacted in March. And with the United States recording its largest monthly deficit in history last month, some Republicans have begun to balk at the prospect of another multitrillion-dollar package, calling for more limited relief.

Some Republicans, however, are exploring the possibility of broadening the terms of the stimulus law as an alternative to doling out more funds, but still supporting state and local governments. A small group of Republican senators met on Tuesday with Mr. Trump and top administration officials to discuss giving more flexibility in spending previously allocated funds.

Senator John Kennedy, Republican of Louisiana, said in a statement that he had requested the meeting to discuss his proposal, which would eliminate guardrails set on the $150 billion sum in the stimulus law, but prohibit the use of the aid for shoring up pension programs.

“This is not something designed to deal with reality, but designed to deal with aspirations,” Mr. McConnell said of the Democrats’ proposal, adding that he would begin discussions with them once Republicans and the White House agreed on how to proceed. “We’re going to insist on doing narrowly targeted legislation

Mr. McConnell said that he and Senator John Cornyn, Republican of Texas, are leading discussions on liability shields for businesses, which would raise the threshold for virus-related malpractice lawsuits and provide new legal protections for companies, government agencies and nonprofit organizations that open during the pandemic.

Democrats have rejected the idea, arguing that the priority should be protecting workers. Senator Chuck Schumer of New York, the Democratic leader, said on Tuesday that only public pressure would shift Republicans from their wait-and-see posture.

Frequently Asked Questions and Advice

Updated June 5, 2020

How many people have lost their jobs due to coronavirus in the U.S.?

The unemployment rate fell to 13.3 percent in May, the Labor Department said on June 5, an unexpected improvement in the nation’s job market as hiring rebounded faster than economists expected. Economists had forecast the unemployment rate to increase to as much as 20 percent, after it hit 14.7 percent in April, which was the highest since the government began keeping official statistics after World War II. But the unemployment rate dipped instead, with employers adding 2.5 million jobs, after more than 20 million jobs were lost in April.

Will protests set off a second viral wave of coronavirus?

Mass protests against police brutality that have brought thousands of people onto the streets in cities across America are raising the specter of new coronavirus outbreaks, prompting political leaders, physicians and public health experts to warn that the crowds could cause a surge in cases. While many political leaders affirmed the right of protesters to express themselves, they urged the demonstrators to wear face masks and maintain social distancing, both to protect themselves and to prevent further community spread of the virus. Some infectious disease experts were reassured by the fact that the protests were held outdoors, saying the open air settings could mitigate the risk of transmission.

How do we start exercising again without hurting ourselves after months of lockdown?

Exercise researchers and physicians have some blunt advice for those of us aiming to return to regular exercise now: Start slowly and then rev up your workouts, also slowly. American adults tended to be about 12 percent less active after the stay-at-home mandates began in March than they were in January. But there are steps you can take to ease your way back into regular exercise safely. First, “start at no more than 50 percent of the exercise you were doing before Covid,” says Dr. Monica Rho, the chief of musculoskeletal medicine at the Shirley Ryan AbilityLab in Chicago. Thread in some preparatory squats, too, she advises. “When you haven’t been exercising, you lose muscle mass.” Expect some muscle twinges after these preliminary, post-lockdown sessions, especially a day or two later. But sudden or increasing pain during exercise is a clarion call to stop and return home.

My state is reopening. Is it safe to go out?

States are reopening bit by bit. This means that more public spaces are available for use and more and more businesses are being allowed to open again. The federal government is largely leaving the decision up to states, and some state leaders are leaving the decision up to local authorities. Even if you aren’t being told to stay at home, it’s still a good idea to limit trips outside and your interaction with other people.

What’s the risk of catching coronavirus from a surface?

Touching contaminated objects and then infecting ourselves with the germs is not typically how the virus spreads. But it can happen. A number of studies of flu, rhinovirus, coronavirus and other microbes have shown that respiratory illnesses, including the new coronavirus, can spread by touching contaminated surfaces, particularly in places like day care centers, offices and hospitals. But a long chain of events has to happen for the disease to spread that way. The best way to protect yourself from coronavirus — whether it’s surface transmission or close human contact — is still social distancing, washing your hands, not touching your face and wearing masks.

How can I protect myself while flying?

If air travel is unavoidable, there are some steps you can take to protect yourself. Most important: Wash your hands often, and stop touching your face. If possible, choose a window seat. A study from Emory University found that during flu season, the safest place to sit on a plane is by a window, as people sitting in window seats had less contact with potentially sick people. Disinfect hard surfaces. When you get to your seat and your hands are clean, use disinfecting wipes to clean the hard surfaces at your seat like the head and arm rest, the seatbelt buckle, the remote, screen, seat back pocket and the tray table. If the seat is hard and nonporous or leather or pleather, you can wipe that down, too. (Using wipes on upholstered seats could lead to a wet seat and spreading of germs rather than killing them.)

Should I wear a mask?

The C.D.C. has recommended that all Americans wear cloth masks if they go out in public. This is a shift in federal guidance reflecting new concerns that the coronavirus is being spread by infected people who have no symptoms. Until now, the C.D.C., like the W.H.O., has advised that ordinary people don’t need to wear masks unless they are sick and coughing. Part of the reason was to preserve medical-grade masks for health care workers who desperately need them at a time when they are in continuously short supply. Masks don’t replace hand washing and social distancing.

What should I do if I feel sick?

If you’ve been exposed to the coronavirus or think you have, and have a fever or symptoms like a cough or difficulty breathing, call a doctor. They should give you advice on whether you should be tested, how to get tested, and how to seek medical treatment without potentially infecting or exposing others.

In the legislation unveiled Tuesday, Democrats included provisions intended to provide more protections for essential workers. The bill would also provide for $75 billion in mortgage relief and $100 billion for rental assistance. It would substantially expand eligibility and increase the value of some tax credits targeted to the poorest Americans, like the earned-income tax credit.

The bill would temporarily suspend a limit on the deduction of state and local taxes from federal income taxes, a move that would disproportionately benefit high-income taxpayers in high-tax areas, and which Democrats have pushed for since the limit was imposed by Mr. Trump’s signature 2017 tax overhaul.

The bill also proposes rolling back a widely-criticized tax break for the wealthy included in the stimulus package. That provision permits married couples making at least $500,000 a year to use losses in their business to wipe out their tax bills from gains in the stock market.

Some of the most liberal members of the Democratic caucus, however, balked at the proposal, arguing that it fell short of what was needed to salvage the American economy and support vulnerable populations. The Congressional Progressive Caucus urged its members to officially inform party leaders that they were undecided on the measure, effectively threatening to block it. They also called for the vote to be delayed by a week, and for a meeting of all Democrats to discuss the legislation.

“In no circumstance are we ready to vote on this on Friday,” Representative Pramila Jayapal, Democrat of Washington and co-chairwoman of the Congressional Progressive Caucus, said on Tuesday in an interview. “We need a full caucus conversation, an open dialogue, and we need to figure out how to address the crisis with a solution that matches its scale.”

Ms. Jayapal has called for the federal government to guarantee business payrolls, extend emergency health coverage for the uninsured and tie relief funding for states to requirements that they follow guidelines from health experts as they begin to reopen.

She said she grew frustrated on Monday when Ms. Pelosi informed Democrats on a conference call that a payroll guarantee program would not be included in the proposal.

Jim Tankersley and Catie Edmondson contributed reporting from Washington, and Jesse Drucker from New York.